Final answer:
To determine the time needed to earn $500 interest on a $50,000 deposit at a 6% interest rate, the simple interest formula is used, resulting in approximately 2 months.
Step-by-step explanation:
To calculate how long an investor would need to deposit $50,000 at a 6% interest rate to earn $500 in interest, we can use the formula for simple interest: I = PRT, where I is the interest earned, P is the principal amount, R is the interest rate, and T is the time in years.
To find T, we rearrange the formula to T = I / (PR).
Given that I = $500, P = $50,000, and R = 6% or 0.06, we substitute the values into the formula to get T = $500 / ($50,000 × 0.06), which simplifies to T = $500 / $3,000, resulting in T = 0.1667 years. Therefore, it would take approximately 0.1667 years, or about 2 months, to earn $500 interest on a $50,000 deposit at a rate of 6%.